Despite having read dozens of articles discussing Evidential Decision Theory (EDT), I’ve only just figured out a clear and concise explanation of what it is. Taking a step back, let’s look at how this is normally explained and one potential issue with this explanation. All major decision theories (EDT, CDT, FDT) rate potential decisions using expected value calculations where:
Each theory uses a different notion of probability for the outcomes
Each theory uses the same utility function for valuing the outcomes
So it should be just a simple matter of stating what the probability function is. EDT is normally explained as using P(O|S & D) where O is the outcome, S is the prior state and D is the decision. At this point it seems like this couldn’t possibly fail to be what we want. Indeed, if S described all state, then there wouldn’t be the possibility of making the smoking lesion argument.
However, that’s because it fails to differentiate between hidden state and visible state. EDT uses visible state, so we can write it as P(O|V & D). The probability distribution of O actually depends on H as well, ie. it is some function f(V, H, D). In most cases H is uncorrelated with D, but this isn’t always necessarily the case. So what might look like the direct effect of V and D on P might actually turn out to be the indirect effects of D affecting our expected distribution of H then affecting P. For example, in Smoking Lesion, we might see ourselves scoring poorly in the counterfactual where we smoke and we assume that this is because of our decision. However, this ignores the fact that when we smoke, H is likely to contain the lesion and also cancer. So we think we’ve set up a fair playing field for deciding between smoking and non-smoking, but we haven’t because of the differences in H.
Or to summarise: “The decision can correlate with hidden state, which can affect the probability distribution of outcomes”. Maybe this is already obvious to everyone, but this was the key I need to be able to internalise these ideas on an intuitive level.
Despite having read dozens of articles discussing Evidential Decision Theory (EDT), I’ve only just figured out a clear and concise explanation of what it is. Taking a step back, let’s look at how this is normally explained and one potential issue with this explanation. All major decision theories (EDT, CDT, FDT) rate potential decisions using expected value calculations where:
Each theory uses a different notion of probability for the outcomes
Each theory uses the same utility function for valuing the outcomes
So it should be just a simple matter of stating what the probability function is. EDT is normally explained as using P(O|S & D) where O is the outcome, S is the prior state and D is the decision. At this point it seems like this couldn’t possibly fail to be what we want. Indeed, if S described all state, then there wouldn’t be the possibility of making the smoking lesion argument.
However, that’s because it fails to differentiate between hidden state and visible state. EDT uses visible state, so we can write it as P(O|V & D). The probability distribution of O actually depends on H as well, ie. it is some function f(V, H, D). In most cases H is uncorrelated with D, but this isn’t always necessarily the case. So what might look like the direct effect of V and D on P might actually turn out to be the indirect effects of D affecting our expected distribution of H then affecting P. For example, in Smoking Lesion, we might see ourselves scoring poorly in the counterfactual where we smoke and we assume that this is because of our decision. However, this ignores the fact that when we smoke, H is likely to contain the lesion and also cancer. So we think we’ve set up a fair playing field for deciding between smoking and non-smoking, but we haven’t because of the differences in H.
Or to summarise: “The decision can correlate with hidden state, which can affect the probability distribution of outcomes”. Maybe this is already obvious to everyone, but this was the key I need to be able to internalise these ideas on an intuitive level.